1/2 Step Out of Tune

Bought my first bass a few days ago. Was doing an appregio in E when I noticed the E string to be out of tune.

In the open position the E string is in tune. Tuned it with an electronic tuner, and it sounds fine playing octaves, etc.

However, if I play, E, G#, B, E, the G# turns out to be an A. I even checked it with the tuner. If I press the third fret, G, the tuner registers and G#, if I play an G#, the tuner registers an A, and so on.

I then tuned down the E string to Eb just to see how an E appergio would sound. The G# sounded as it should, but of course the open E string was out of tune.

Is this something I can fix myself, or should I bring it back to the store, and let them deal with it.